Extraction and analysis of transient signals of a deployable structure vibration based on the sparse decomposition with mixed norms

Abstract

This contribution deals with extraction and analysis of the transient component of a deployable structure vibration based on the sparse decomposition with mixed norms. The transient component is a critical nonlinear dynamical characteristic of the deployable structure. However, extraction of weak transient signals has always been a challenging problem in signal processing. To resolve this problem, we present an algorithm based on the sparse decomposition with the mixed norm. As redundant components may occur in the sparse decomposition, resulting from the end effect of time-frequency representations. Flip mirror extension is designed to address this question. The feasibilities of the short time Fourier transform, the Wigner-Ville distribution, the ensemble empirical mode decomposition, the stationary wavelet transform and the presented method to catch the transient component are verified with a sample example, and the result shows that the presented algorithm is more powerful. After that, the method is employed to extract transients from experimental signals of a deployable structure model; furthermore, characteristics of these components are analyzed, and are as follows: the transient components are complicated; the transient amplitudes decrease as a whole; the transient amplitudes are locally random. The algorithm is valuable for extracting the transient component from the vibrations, and the analysis may be valuable for the analysis of the nonlinear dynamics of the deployable structure.